Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,8,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(178.059464526\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3046x^{2} + 50476x + 497070 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(36.0320\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −125.000 | −0.447214 | ||||||||
\(6\) | 216.000 | 0.408248 | ||||||||
\(7\) | 218.883 | 0.241195 | 0.120597 | − | 0.992701i | \(-0.461519\pi\) | ||||
0.120597 | + | 0.992701i | \(0.461519\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −1000.00 | −0.316228 | ||||||||
\(11\) | 2680.26 | 0.607160 | 0.303580 | − | 0.952806i | \(-0.401818\pi\) | ||||
0.303580 | + | 0.952806i | \(0.401818\pi\) | |||||||
\(12\) | 1728.00 | 0.288675 | ||||||||
\(13\) | −12154.8 | −1.53442 | −0.767211 | − | 0.641394i | \(-0.778356\pi\) | ||||
−0.767211 | + | 0.641394i | \(0.778356\pi\) | |||||||
\(14\) | 1751.06 | 0.170550 | ||||||||
\(15\) | −3375.00 | −0.258199 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −17716.1 | −0.874573 | −0.437286 | − | 0.899322i | \(-0.644060\pi\) | ||||
−0.437286 | + | 0.899322i | \(0.644060\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | 6859.00 | 0.229416 | ||||||||
\(20\) | −8000.00 | −0.223607 | ||||||||
\(21\) | 5909.83 | 0.139254 | ||||||||
\(22\) | 21442.1 | 0.429327 | ||||||||
\(23\) | 61090.5 | 1.04695 | 0.523475 | − | 0.852041i | \(-0.324635\pi\) | ||||
0.523475 | + | 0.852041i | \(0.324635\pi\) | |||||||
\(24\) | 13824.0 | 0.204124 | ||||||||
\(25\) | 15625.0 | 0.200000 | ||||||||
\(26\) | −97238.2 | −1.08500 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 14008.5 | 0.120597 | ||||||||
\(29\) | −50427.7 | −0.383951 | −0.191976 | − | 0.981400i | \(-0.561489\pi\) | ||||
−0.191976 | + | 0.981400i | \(0.561489\pi\) | |||||||
\(30\) | −27000.0 | −0.182574 | ||||||||
\(31\) | 18940.3 | 0.114188 | 0.0570940 | − | 0.998369i | \(-0.481817\pi\) | ||||
0.0570940 | + | 0.998369i | \(0.481817\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | 72367.1 | 0.350544 | ||||||||
\(34\) | −141729. | −0.618416 | ||||||||
\(35\) | −27360.3 | −0.107866 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | −375078. | −1.21735 | −0.608675 | − | 0.793419i | \(-0.708299\pi\) | ||||
−0.608675 | + | 0.793419i | \(0.708299\pi\) | |||||||
\(38\) | 54872.0 | 0.162221 | ||||||||
\(39\) | −328179. | −0.885899 | ||||||||
\(40\) | −64000.0 | −0.158114 | ||||||||
\(41\) | 16560.1 | 0.0375249 | 0.0187624 | − | 0.999824i | \(-0.494027\pi\) | ||||
0.0187624 | + | 0.999824i | \(0.494027\pi\) | |||||||
\(42\) | 47278.6 | 0.0984674 | ||||||||
\(43\) | −9999.12 | −0.0191788 | −0.00958942 | − | 0.999954i | \(-0.503052\pi\) | ||||
−0.00958942 | + | 0.999954i | \(0.503052\pi\) | |||||||
\(44\) | 171537. | 0.303580 | ||||||||
\(45\) | −91125.0 | −0.149071 | ||||||||
\(46\) | 488724. | 0.740306 | ||||||||
\(47\) | −931134. | −1.30819 | −0.654093 | − | 0.756414i | \(-0.726950\pi\) | ||||
−0.654093 | + | 0.756414i | \(0.726950\pi\) | |||||||
\(48\) | 110592. | 0.144338 | ||||||||
\(49\) | −775633. | −0.941825 | ||||||||
\(50\) | 125000. | 0.141421 | ||||||||
\(51\) | −478334. | −0.504935 | ||||||||
\(52\) | −777905. | −0.767211 | ||||||||
\(53\) | −1.38828e6 | −1.28088 | −0.640442 | − | 0.768006i | \(-0.721249\pi\) | ||||
−0.640442 | + | 0.768006i | \(0.721249\pi\) | |||||||
\(54\) | 157464. | 0.136083 | ||||||||
\(55\) | −335033. | −0.271530 | ||||||||
\(56\) | 112068. | 0.0852752 | ||||||||
\(57\) | 185193. | 0.132453 | ||||||||
\(58\) | −403421. | −0.271494 | ||||||||
\(59\) | 1.24289e6 | 0.787865 | 0.393932 | − | 0.919139i | \(-0.371114\pi\) | ||||
0.393932 | + | 0.919139i | \(0.371114\pi\) | |||||||
\(60\) | −216000. | −0.129099 | ||||||||
\(61\) | 1.98086e6 | 1.11738 | 0.558689 | − | 0.829377i | \(-0.311305\pi\) | ||||
0.558689 | + | 0.829377i | \(0.311305\pi\) | |||||||
\(62\) | 151522. | 0.0807432 | ||||||||
\(63\) | 159565. | 0.0803983 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 1.51935e6 | 0.686215 | ||||||||
\(66\) | 578937. | 0.247872 | ||||||||
\(67\) | 1.61129e6 | 0.654502 | 0.327251 | − | 0.944938i | \(-0.393878\pi\) | ||||
0.327251 | + | 0.944938i | \(0.393878\pi\) | |||||||
\(68\) | −1.13383e6 | −0.437286 | ||||||||
\(69\) | 1.64944e6 | 0.604457 | ||||||||
\(70\) | −218883. | −0.0762725 | ||||||||
\(71\) | −5.75895e6 | −1.90959 | −0.954793 | − | 0.297272i | \(-0.903923\pi\) | ||||
−0.954793 | + | 0.297272i | \(0.903923\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | 1.60335e6 | 0.482391 | 0.241195 | − | 0.970477i | \(-0.422461\pi\) | ||||
0.241195 | + | 0.970477i | \(0.422461\pi\) | |||||||
\(74\) | −3.00063e6 | −0.860797 | ||||||||
\(75\) | 421875. | 0.115470 | ||||||||
\(76\) | 438976. | 0.114708 | ||||||||
\(77\) | 586663. | 0.146444 | ||||||||
\(78\) | −2.62543e6 | −0.626425 | ||||||||
\(79\) | −2.22482e6 | −0.507692 | −0.253846 | − | 0.967245i | \(-0.581696\pi\) | ||||
−0.253846 | + | 0.967245i | \(0.581696\pi\) | |||||||
\(80\) | −512000. | −0.111803 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 132481. | 0.0265341 | ||||||||
\(83\) | −1.73453e6 | −0.332973 | −0.166486 | − | 0.986044i | \(-0.553242\pi\) | ||||
−0.166486 | + | 0.986044i | \(0.553242\pi\) | |||||||
\(84\) | 378229. | 0.0696269 | ||||||||
\(85\) | 2.21451e6 | 0.391121 | ||||||||
\(86\) | −79993.0 | −0.0135615 | ||||||||
\(87\) | −1.36155e6 | −0.221674 | ||||||||
\(88\) | 1.37229e6 | 0.214663 | ||||||||
\(89\) | −1.31072e6 | −0.197081 | −0.0985407 | − | 0.995133i | \(-0.531417\pi\) | ||||
−0.0985407 | + | 0.995133i | \(0.531417\pi\) | |||||||
\(90\) | −729000. | −0.105409 | ||||||||
\(91\) | −2.66047e6 | −0.370095 | ||||||||
\(92\) | 3.90979e6 | 0.523475 | ||||||||
\(93\) | 511388. | 0.0659265 | ||||||||
\(94\) | −7.44907e6 | −0.925028 | ||||||||
\(95\) | −857375. | −0.102598 | ||||||||
\(96\) | 884736. | 0.102062 | ||||||||
\(97\) | 8.90120e6 | 0.990256 | 0.495128 | − | 0.868820i | \(-0.335121\pi\) | ||||
0.495128 | + | 0.868820i | \(0.335121\pi\) | |||||||
\(98\) | −6.20507e6 | −0.665971 | ||||||||
\(99\) | 1.95391e6 | 0.202387 | ||||||||
\(100\) | 1.00000e6 | 0.100000 | ||||||||
\(101\) | −1.89951e7 | −1.83450 | −0.917249 | − | 0.398315i | \(-0.869595\pi\) | ||||
−0.917249 | + | 0.398315i | \(0.869595\pi\) | |||||||
\(102\) | −3.82667e6 | −0.357043 | ||||||||
\(103\) | 1.05914e6 | 0.0955042 | 0.0477521 | − | 0.998859i | \(-0.484794\pi\) | ||||
0.0477521 | + | 0.998859i | \(0.484794\pi\) | |||||||
\(104\) | −6.22324e6 | −0.542500 | ||||||||
\(105\) | −738729. | −0.0622762 | ||||||||
\(106\) | −1.11062e7 | −0.905722 | ||||||||
\(107\) | −7.98725e6 | −0.630310 | −0.315155 | − | 0.949040i | \(-0.602057\pi\) | ||||
−0.315155 | + | 0.949040i | \(0.602057\pi\) | |||||||
\(108\) | 1.25971e6 | 0.0962250 | ||||||||
\(109\) | −9.55047e6 | −0.706369 | −0.353185 | − | 0.935554i | \(-0.614901\pi\) | ||||
−0.353185 | + | 0.935554i | \(0.614901\pi\) | |||||||
\(110\) | −2.68026e6 | −0.192001 | ||||||||
\(111\) | −1.01271e7 | −0.702838 | ||||||||
\(112\) | 896543. | 0.0602987 | ||||||||
\(113\) | 1.67736e7 | 1.09358 | 0.546790 | − | 0.837270i | \(-0.315850\pi\) | ||||
0.546790 | + | 0.837270i | \(0.315850\pi\) | |||||||
\(114\) | 1.48154e6 | 0.0936586 | ||||||||
\(115\) | −7.63631e6 | −0.468211 | ||||||||
\(116\) | −3.22737e6 | −0.191976 | ||||||||
\(117\) | −8.86083e6 | −0.511474 | ||||||||
\(118\) | 9.94315e6 | 0.557105 | ||||||||
\(119\) | −3.87774e6 | −0.210942 | ||||||||
\(120\) | −1.72800e6 | −0.0912871 | ||||||||
\(121\) | −1.23034e7 | −0.631357 | ||||||||
\(122\) | 1.58469e7 | 0.790106 | ||||||||
\(123\) | 447123. | 0.0216650 | ||||||||
\(124\) | 1.21218e6 | 0.0570940 | ||||||||
\(125\) | −1.95312e6 | −0.0894427 | ||||||||
\(126\) | 1.27652e6 | 0.0568502 | ||||||||
\(127\) | −1.47405e7 | −0.638558 | −0.319279 | − | 0.947661i | \(-0.603441\pi\) | ||||
−0.319279 | + | 0.947661i | \(0.603441\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −269976. | −0.0110729 | ||||||||
\(130\) | 1.21548e7 | 0.485227 | ||||||||
\(131\) | −1.05608e6 | −0.0410436 | −0.0205218 | − | 0.999789i | \(-0.506533\pi\) | ||||
−0.0205218 | + | 0.999789i | \(0.506533\pi\) | |||||||
\(132\) | 4.63150e6 | 0.175272 | ||||||||
\(133\) | 1.50132e6 | 0.0553339 | ||||||||
\(134\) | 1.28903e7 | 0.462802 | ||||||||
\(135\) | −2.46038e6 | −0.0860663 | ||||||||
\(136\) | −9.07063e6 | −0.309208 | ||||||||
\(137\) | 9.05173e6 | 0.300753 | 0.150376 | − | 0.988629i | \(-0.451951\pi\) | ||||
0.150376 | + | 0.988629i | \(0.451951\pi\) | |||||||
\(138\) | 1.31955e7 | 0.427416 | ||||||||
\(139\) | −4.40231e7 | −1.39037 | −0.695183 | − | 0.718833i | \(-0.744676\pi\) | ||||
−0.695183 | + | 0.718833i | \(0.744676\pi\) | |||||||
\(140\) | −1.75106e6 | −0.0539328 | ||||||||
\(141\) | −2.51406e7 | −0.755282 | ||||||||
\(142\) | −4.60716e7 | −1.35028 | ||||||||
\(143\) | −3.25780e7 | −0.931640 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | 6.30346e6 | 0.171708 | ||||||||
\(146\) | 1.28268e7 | 0.341102 | ||||||||
\(147\) | −2.09421e7 | −0.543763 | ||||||||
\(148\) | −2.40050e7 | −0.608675 | ||||||||
\(149\) | 2.40592e7 | 0.595839 | 0.297920 | − | 0.954591i | \(-0.403707\pi\) | ||||
0.297920 | + | 0.954591i | \(0.403707\pi\) | |||||||
\(150\) | 3.37500e6 | 0.0816497 | ||||||||
\(151\) | −4.28905e7 | −1.01378 | −0.506888 | − | 0.862012i | \(-0.669204\pi\) | ||||
−0.506888 | + | 0.862012i | \(0.669204\pi\) | |||||||
\(152\) | 3.51181e6 | 0.0811107 | ||||||||
\(153\) | −1.29150e7 | −0.291524 | ||||||||
\(154\) | 4.69330e6 | 0.103551 | ||||||||
\(155\) | −2.36754e6 | −0.0510665 | ||||||||
\(156\) | −2.10034e7 | −0.442950 | ||||||||
\(157\) | 2.54178e7 | 0.524191 | 0.262096 | − | 0.965042i | \(-0.415586\pi\) | ||||
0.262096 | + | 0.965042i | \(0.415586\pi\) | |||||||
\(158\) | −1.77986e7 | −0.358993 | ||||||||
\(159\) | −3.74834e7 | −0.739519 | ||||||||
\(160\) | −4.09600e6 | −0.0790569 | ||||||||
\(161\) | 1.33716e7 | 0.252519 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | 1.31342e7 | 0.237546 | 0.118773 | − | 0.992921i | \(-0.462104\pi\) | ||||
0.118773 | + | 0.992921i | \(0.462104\pi\) | |||||||
\(164\) | 1.05985e6 | 0.0187624 | ||||||||
\(165\) | −9.04589e6 | −0.156768 | ||||||||
\(166\) | −1.38762e7 | −0.235447 | ||||||||
\(167\) | 1.66839e7 | 0.277198 | 0.138599 | − | 0.990349i | \(-0.455740\pi\) | ||||
0.138599 | + | 0.990349i | \(0.455740\pi\) | |||||||
\(168\) | 3.02583e6 | 0.0492337 | ||||||||
\(169\) | 8.49899e7 | 1.35445 | ||||||||
\(170\) | 1.77161e7 | 0.276564 | ||||||||
\(171\) | 5.00021e6 | 0.0764719 | ||||||||
\(172\) | −639944. | −0.00958942 | ||||||||
\(173\) | −3.14081e7 | −0.461191 | −0.230595 | − | 0.973050i | \(-0.574067\pi\) | ||||
−0.230595 | + | 0.973050i | \(0.574067\pi\) | |||||||
\(174\) | −1.08924e7 | −0.156747 | ||||||||
\(175\) | 3.42004e6 | 0.0482390 | ||||||||
\(176\) | 1.09784e7 | 0.151790 | ||||||||
\(177\) | 3.35581e7 | 0.454874 | ||||||||
\(178\) | −1.04858e7 | −0.139358 | ||||||||
\(179\) | −3.56579e7 | −0.464698 | −0.232349 | − | 0.972633i | \(-0.574641\pi\) | ||||
−0.232349 | + | 0.972633i | \(0.574641\pi\) | |||||||
\(180\) | −5.83200e6 | −0.0745356 | ||||||||
\(181\) | −8.86947e7 | −1.11179 | −0.555895 | − | 0.831253i | \(-0.687624\pi\) | ||||
−0.555895 | + | 0.831253i | \(0.687624\pi\) | |||||||
\(182\) | −2.12837e7 | −0.261697 | ||||||||
\(183\) | 5.34833e7 | 0.645119 | ||||||||
\(184\) | 3.12783e7 | 0.370153 | ||||||||
\(185\) | 4.68848e7 | 0.544416 | ||||||||
\(186\) | 4.09110e6 | 0.0466171 | ||||||||
\(187\) | −4.74837e7 | −0.531006 | ||||||||
\(188\) | −5.95926e7 | −0.654093 | ||||||||
\(189\) | 4.30827e6 | 0.0464180 | ||||||||
\(190\) | −6.85900e6 | −0.0725476 | ||||||||
\(191\) | 4.33253e7 | 0.449909 | 0.224954 | − | 0.974369i | \(-0.427777\pi\) | ||||
0.224954 | + | 0.974369i | \(0.427777\pi\) | |||||||
\(192\) | 7.07789e6 | 0.0721688 | ||||||||
\(193\) | −3.27194e7 | −0.327608 | −0.163804 | − | 0.986493i | \(-0.552377\pi\) | ||||
−0.163804 | + | 0.986493i | \(0.552377\pi\) | |||||||
\(194\) | 7.12096e7 | 0.700216 | ||||||||
\(195\) | 4.10223e7 | 0.396186 | ||||||||
\(196\) | −4.96405e7 | −0.470913 | ||||||||
\(197\) | 2.52473e7 | 0.235279 | 0.117639 | − | 0.993056i | \(-0.462467\pi\) | ||||
0.117639 | + | 0.993056i | \(0.462467\pi\) | |||||||
\(198\) | 1.56313e7 | 0.143109 | ||||||||
\(199\) | −1.77828e8 | −1.59961 | −0.799806 | − | 0.600259i | \(-0.795064\pi\) | ||||
−0.799806 | + | 0.600259i | \(0.795064\pi\) | |||||||
\(200\) | 8.00000e6 | 0.0707107 | ||||||||
\(201\) | 4.35047e7 | 0.377877 | ||||||||
\(202\) | −1.51961e8 | −1.29719 | ||||||||
\(203\) | −1.10377e7 | −0.0926070 | ||||||||
\(204\) | −3.06134e7 | −0.252467 | ||||||||
\(205\) | −2.07001e6 | −0.0167816 | ||||||||
\(206\) | 8.47311e6 | 0.0675317 | ||||||||
\(207\) | 4.45350e7 | 0.348984 | ||||||||
\(208\) | −4.97859e7 | −0.383606 | ||||||||
\(209\) | 1.83839e7 | 0.139292 | ||||||||
\(210\) | −5.90983e6 | −0.0440359 | ||||||||
\(211\) | −4.30155e7 | −0.315236 | −0.157618 | − | 0.987500i | \(-0.550382\pi\) | ||||
−0.157618 | + | 0.987500i | \(0.550382\pi\) | |||||||
\(212\) | −8.88496e7 | −0.640442 | ||||||||
\(213\) | −1.55492e8 | −1.10250 | ||||||||
\(214\) | −6.38980e7 | −0.445696 | ||||||||
\(215\) | 1.24989e6 | 0.00857704 | ||||||||
\(216\) | 1.00777e7 | 0.0680414 | ||||||||
\(217\) | 4.14570e6 | 0.0275416 | ||||||||
\(218\) | −7.64037e7 | −0.499479 | ||||||||
\(219\) | 4.32905e7 | 0.278508 | ||||||||
\(220\) | −2.14421e7 | −0.135765 | ||||||||
\(221\) | 2.15335e8 | 1.34196 | ||||||||
\(222\) | −8.10169e7 | −0.496981 | ||||||||
\(223\) | 1.28014e8 | 0.773019 | 0.386510 | − | 0.922285i | \(-0.373681\pi\) | ||||
0.386510 | + | 0.922285i | \(0.373681\pi\) | |||||||
\(224\) | 7.17234e6 | 0.0426376 | ||||||||
\(225\) | 1.13906e7 | 0.0666667 | ||||||||
\(226\) | 1.34189e8 | 0.773278 | ||||||||
\(227\) | 8.82730e7 | 0.500884 | 0.250442 | − | 0.968132i | \(-0.419424\pi\) | ||||
0.250442 | + | 0.968132i | \(0.419424\pi\) | |||||||
\(228\) | 1.18524e7 | 0.0662266 | ||||||||
\(229\) | 2.34752e6 | 0.0129177 | 0.00645885 | − | 0.999979i | \(-0.497944\pi\) | ||||
0.00645885 | + | 0.999979i | \(0.497944\pi\) | |||||||
\(230\) | −6.10905e7 | −0.331075 | ||||||||
\(231\) | 1.58399e7 | 0.0845494 | ||||||||
\(232\) | −2.58190e7 | −0.135747 | ||||||||
\(233\) | −2.06062e8 | −1.06722 | −0.533609 | − | 0.845731i | \(-0.679165\pi\) | ||||
−0.533609 | + | 0.845731i | \(0.679165\pi\) | |||||||
\(234\) | −7.08866e7 | −0.361667 | ||||||||
\(235\) | 1.16392e8 | 0.585039 | ||||||||
\(236\) | 7.95452e7 | 0.393932 | ||||||||
\(237\) | −6.00702e7 | −0.293116 | ||||||||
\(238\) | −3.10219e7 | −0.149159 | ||||||||
\(239\) | −1.44459e8 | −0.684466 | −0.342233 | − | 0.939615i | \(-0.611183\pi\) | ||||
−0.342233 | + | 0.939615i | \(0.611183\pi\) | |||||||
\(240\) | −1.38240e7 | −0.0645497 | ||||||||
\(241\) | 1.38118e8 | 0.635608 | 0.317804 | − | 0.948156i | \(-0.397055\pi\) | ||||
0.317804 | + | 0.948156i | \(0.397055\pi\) | |||||||
\(242\) | −9.84269e7 | −0.446437 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 1.26775e8 | 0.558689 | ||||||||
\(245\) | 9.69542e7 | 0.421197 | ||||||||
\(246\) | 3.57698e6 | 0.0153195 | ||||||||
\(247\) | −8.33696e7 | −0.352021 | ||||||||
\(248\) | 9.69743e6 | 0.0403716 | ||||||||
\(249\) | −4.68323e7 | −0.192242 | ||||||||
\(250\) | −1.56250e7 | −0.0632456 | ||||||||
\(251\) | −1.44952e8 | −0.578584 | −0.289292 | − | 0.957241i | \(-0.593420\pi\) | ||||
−0.289292 | + | 0.957241i | \(0.593420\pi\) | |||||||
\(252\) | 1.02122e7 | 0.0401991 | ||||||||
\(253\) | 1.63739e8 | 0.635667 | ||||||||
\(254\) | −1.17924e8 | −0.451529 | ||||||||
\(255\) | 5.97917e7 | 0.225814 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 5.91829e7 | 0.217486 | 0.108743 | − | 0.994070i | \(-0.465318\pi\) | ||||
0.108743 | + | 0.994070i | \(0.465318\pi\) | |||||||
\(258\) | −2.15981e6 | −0.00782973 | ||||||||
\(259\) | −8.20981e7 | −0.293619 | ||||||||
\(260\) | 9.72382e7 | 0.343107 | ||||||||
\(261\) | −3.67618e7 | −0.127984 | ||||||||
\(262\) | −8.44861e6 | −0.0290222 | ||||||||
\(263\) | −2.51555e8 | −0.852685 | −0.426343 | − | 0.904562i | \(-0.640198\pi\) | ||||
−0.426343 | + | 0.904562i | \(0.640198\pi\) | |||||||
\(264\) | 3.70520e7 | 0.123936 | ||||||||
\(265\) | 1.73534e8 | 0.572829 | ||||||||
\(266\) | 1.20105e7 | 0.0391270 | ||||||||
\(267\) | −3.53895e7 | −0.113785 | ||||||||
\(268\) | 1.03122e8 | 0.327251 | ||||||||
\(269\) | −2.42927e8 | −0.760927 | −0.380464 | − | 0.924796i | \(-0.624236\pi\) | ||||
−0.380464 | + | 0.924796i | \(0.624236\pi\) | |||||||
\(270\) | −1.96830e7 | −0.0608581 | ||||||||
\(271\) | −2.79870e8 | −0.854209 | −0.427104 | − | 0.904202i | \(-0.640466\pi\) | ||||
−0.427104 | + | 0.904202i | \(0.640466\pi\) | |||||||
\(272\) | −7.25650e7 | −0.218643 | ||||||||
\(273\) | −7.18326e7 | −0.213674 | ||||||||
\(274\) | 7.24139e7 | 0.212664 | ||||||||
\(275\) | 4.18791e7 | 0.121432 | ||||||||
\(276\) | 1.05564e8 | 0.302229 | ||||||||
\(277\) | −4.13906e8 | −1.17010 | −0.585049 | − | 0.810998i | \(-0.698925\pi\) | ||||
−0.585049 | + | 0.810998i | \(0.698925\pi\) | |||||||
\(278\) | −3.52185e8 | −0.983137 | ||||||||
\(279\) | 1.38075e7 | 0.0380627 | ||||||||
\(280\) | −1.40085e7 | −0.0381363 | ||||||||
\(281\) | −1.15682e8 | −0.311025 | −0.155512 | − | 0.987834i | \(-0.549703\pi\) | ||||
−0.155512 | + | 0.987834i | \(0.549703\pi\) | |||||||
\(282\) | −2.01125e8 | −0.534065 | ||||||||
\(283\) | 4.76235e8 | 1.24902 | 0.624509 | − | 0.781018i | \(-0.285299\pi\) | ||||
0.624509 | + | 0.781018i | \(0.285299\pi\) | |||||||
\(284\) | −3.68573e8 | −0.954793 | ||||||||
\(285\) | −2.31491e7 | −0.0592349 | ||||||||
\(286\) | −2.60624e8 | −0.658769 | ||||||||
\(287\) | 3.62472e6 | 0.00905081 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | −9.64797e7 | −0.235122 | ||||||||
\(290\) | 5.04277e7 | 0.121416 | ||||||||
\(291\) | 2.40332e8 | 0.571724 | ||||||||
\(292\) | 1.02615e8 | 0.241195 | ||||||||
\(293\) | 3.99799e8 | 0.928551 | 0.464275 | − | 0.885691i | \(-0.346315\pi\) | ||||
0.464275 | + | 0.885691i | \(0.346315\pi\) | |||||||
\(294\) | −1.67537e8 | −0.384498 | ||||||||
\(295\) | −1.55362e8 | −0.352344 | ||||||||
\(296\) | −1.92040e8 | −0.430399 | ||||||||
\(297\) | 5.27556e7 | 0.116848 | ||||||||
\(298\) | 1.92474e8 | 0.421322 | ||||||||
\(299\) | −7.42541e8 | −1.60647 | ||||||||
\(300\) | 2.70000e7 | 0.0577350 | ||||||||
\(301\) | −2.18863e6 | −0.00462584 | ||||||||
\(302\) | −3.43124e8 | −0.716848 | ||||||||
\(303\) | −5.12868e8 | −1.05915 | ||||||||
\(304\) | 2.80945e7 | 0.0573539 | ||||||||
\(305\) | −2.47608e8 | −0.499707 | ||||||||
\(306\) | −1.03320e8 | −0.206139 | ||||||||
\(307\) | −3.94980e8 | −0.779096 | −0.389548 | − | 0.921006i | \(-0.627369\pi\) | ||||
−0.389548 | + | 0.921006i | \(0.627369\pi\) | |||||||
\(308\) | 3.75464e7 | 0.0732219 | ||||||||
\(309\) | 2.85967e7 | 0.0551394 | ||||||||
\(310\) | −1.89403e7 | −0.0361094 | ||||||||
\(311\) | 2.04626e7 | 0.0385744 | 0.0192872 | − | 0.999814i | \(-0.493860\pi\) | ||||
0.0192872 | + | 0.999814i | \(0.493860\pi\) | |||||||
\(312\) | −1.68028e8 | −0.313213 | ||||||||
\(313\) | −8.08100e7 | −0.148957 | −0.0744784 | − | 0.997223i | \(-0.523729\pi\) | ||||
−0.0744784 | + | 0.997223i | \(0.523729\pi\) | |||||||
\(314\) | 2.03343e8 | 0.370659 | ||||||||
\(315\) | −1.99457e7 | −0.0359552 | ||||||||
\(316\) | −1.42389e8 | −0.253846 | ||||||||
\(317\) | 1.03352e9 | 1.82226 | 0.911132 | − | 0.412115i | \(-0.135210\pi\) | ||||
0.911132 | + | 0.412115i | \(0.135210\pi\) | |||||||
\(318\) | −2.99867e8 | −0.522919 | ||||||||
\(319\) | −1.35159e8 | −0.233120 | ||||||||
\(320\) | −3.27680e7 | −0.0559017 | ||||||||
\(321\) | −2.15656e8 | −0.363910 | ||||||||
\(322\) | 1.06973e8 | 0.178558 | ||||||||
\(323\) | −1.21514e8 | −0.200641 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −1.89918e8 | −0.306885 | ||||||||
\(326\) | 1.05074e8 | 0.167970 | ||||||||
\(327\) | −2.57863e8 | −0.407823 | ||||||||
\(328\) | 8.47877e6 | 0.0132671 | ||||||||
\(329\) | −2.03809e8 | −0.315528 | ||||||||
\(330\) | −7.23671e7 | −0.110852 | ||||||||
\(331\) | 2.46710e8 | 0.373929 | 0.186965 | − | 0.982367i | \(-0.440135\pi\) | ||||
0.186965 | + | 0.982367i | \(0.440135\pi\) | |||||||
\(332\) | −1.11010e8 | −0.166486 | ||||||||
\(333\) | −2.73432e8 | −0.405784 | ||||||||
\(334\) | 1.33471e8 | 0.196008 | ||||||||
\(335\) | −2.01411e8 | −0.292702 | ||||||||
\(336\) | 2.42067e7 | 0.0348135 | ||||||||
\(337\) | −7.59669e8 | −1.08123 | −0.540617 | − | 0.841269i | \(-0.681809\pi\) | ||||
−0.540617 | + | 0.841269i | \(0.681809\pi\) | |||||||
\(338\) | 6.79919e8 | 0.957743 | ||||||||
\(339\) | 4.52886e8 | 0.631379 | ||||||||
\(340\) | 1.41729e8 | 0.195560 | ||||||||
\(341\) | 5.07650e7 | 0.0693304 | ||||||||
\(342\) | 4.00017e7 | 0.0540738 | ||||||||
\(343\) | −3.50032e8 | −0.468358 | ||||||||
\(344\) | −5.11955e6 | −0.00678074 | ||||||||
\(345\) | −2.06180e8 | −0.270322 | ||||||||
\(346\) | −2.51265e8 | −0.326111 | ||||||||
\(347\) | 1.31031e9 | 1.68353 | 0.841765 | − | 0.539844i | \(-0.181517\pi\) | ||||
0.841765 | + | 0.539844i | \(0.181517\pi\) | |||||||
\(348\) | −8.71390e7 | −0.110837 | ||||||||
\(349\) | 9.60572e7 | 0.120960 | 0.0604799 | − | 0.998169i | \(-0.480737\pi\) | ||||
0.0604799 | + | 0.998169i | \(0.480737\pi\) | |||||||
\(350\) | 2.73603e7 | 0.0341101 | ||||||||
\(351\) | −2.39242e8 | −0.295300 | ||||||||
\(352\) | 8.78269e7 | 0.107332 | ||||||||
\(353\) | −5.64318e8 | −0.682830 | −0.341415 | − | 0.939913i | \(-0.610906\pi\) | ||||
−0.341415 | + | 0.939913i | \(0.610906\pi\) | |||||||
\(354\) | 2.68465e8 | 0.321645 | ||||||||
\(355\) | 7.19869e8 | 0.853993 | ||||||||
\(356\) | −8.38862e7 | −0.0985407 | ||||||||
\(357\) | −1.04699e8 | −0.121788 | ||||||||
\(358\) | −2.85263e8 | −0.328591 | ||||||||
\(359\) | 2.54090e8 | 0.289839 | 0.144919 | − | 0.989443i | \(-0.453708\pi\) | ||||
0.144919 | + | 0.989443i | \(0.453708\pi\) | |||||||
\(360\) | −4.66560e7 | −0.0527046 | ||||||||
\(361\) | 4.70459e7 | 0.0526316 | ||||||||
\(362\) | −7.09557e8 | −0.786154 | ||||||||
\(363\) | −3.32191e8 | −0.364514 | ||||||||
\(364\) | −1.70270e8 | −0.185047 | ||||||||
\(365\) | −2.00419e8 | −0.215732 | ||||||||
\(366\) | 4.27867e8 | 0.456168 | ||||||||
\(367\) | 4.56848e8 | 0.482437 | 0.241219 | − | 0.970471i | \(-0.422453\pi\) | ||||
0.241219 | + | 0.970471i | \(0.422453\pi\) | |||||||
\(368\) | 2.50227e8 | 0.261738 | ||||||||
\(369\) | 1.20723e7 | 0.0125083 | ||||||||
\(370\) | 3.75078e8 | 0.384960 | ||||||||
\(371\) | −3.03869e8 | −0.308943 | ||||||||
\(372\) | 3.27288e7 | 0.0329633 | ||||||||
\(373\) | −3.12198e8 | −0.311494 | −0.155747 | − | 0.987797i | \(-0.549778\pi\) | ||||
−0.155747 | + | 0.987797i | \(0.549778\pi\) | |||||||
\(374\) | −3.79870e8 | −0.375478 | ||||||||
\(375\) | −5.27344e7 | −0.0516398 | ||||||||
\(376\) | −4.76741e8 | −0.462514 | ||||||||
\(377\) | 6.12937e8 | 0.589143 | ||||||||
\(378\) | 3.44661e7 | 0.0328225 | ||||||||
\(379\) | −2.04152e8 | −0.192626 | −0.0963132 | − | 0.995351i | \(-0.530705\pi\) | ||||
−0.0963132 | + | 0.995351i | \(0.530705\pi\) | |||||||
\(380\) | −5.48720e7 | −0.0512989 | ||||||||
\(381\) | −3.97995e8 | −0.368672 | ||||||||
\(382\) | 3.46602e8 | 0.318134 | ||||||||
\(383\) | 7.91439e8 | 0.719816 | 0.359908 | − | 0.932988i | \(-0.382808\pi\) | ||||
0.359908 | + | 0.932988i | \(0.382808\pi\) | |||||||
\(384\) | 5.66231e7 | 0.0510310 | ||||||||
\(385\) | −7.33329e7 | −0.0654917 | ||||||||
\(386\) | −2.61755e8 | −0.231654 | ||||||||
\(387\) | −7.28936e6 | −0.00639295 | ||||||||
\(388\) | 5.69677e8 | 0.495128 | ||||||||
\(389\) | 3.17457e8 | 0.273439 | 0.136720 | − | 0.990610i | \(-0.456344\pi\) | ||||
0.136720 | + | 0.990610i | \(0.456344\pi\) | |||||||
\(390\) | 3.28179e8 | 0.280146 | ||||||||
\(391\) | −1.08228e9 | −0.915635 | ||||||||
\(392\) | −3.97124e8 | −0.332985 | ||||||||
\(393\) | −2.85141e7 | −0.0236966 | ||||||||
\(394\) | 2.01978e8 | 0.166367 | ||||||||
\(395\) | 2.78103e8 | 0.227047 | ||||||||
\(396\) | 1.25050e8 | 0.101193 | ||||||||
\(397\) | 1.11437e9 | 0.893847 | 0.446924 | − | 0.894572i | \(-0.352520\pi\) | ||||
0.446924 | + | 0.894572i | \(0.352520\pi\) | |||||||
\(398\) | −1.42262e9 | −1.13110 | ||||||||
\(399\) | 4.05355e7 | 0.0319470 | ||||||||
\(400\) | 6.40000e7 | 0.0500000 | ||||||||
\(401\) | 1.04008e9 | 0.805492 | 0.402746 | − | 0.915312i | \(-0.368056\pi\) | ||||
0.402746 | + | 0.915312i | \(0.368056\pi\) | |||||||
\(402\) | 3.48038e8 | 0.267199 | ||||||||
\(403\) | −2.30215e8 | −0.175213 | ||||||||
\(404\) | −1.21569e9 | −0.917249 | ||||||||
\(405\) | −6.64301e7 | −0.0496904 | ||||||||
\(406\) | −8.83019e7 | −0.0654831 | ||||||||
\(407\) | −1.00531e9 | −0.739127 | ||||||||
\(408\) | −2.44907e8 | −0.178521 | ||||||||
\(409\) | 2.25210e8 | 0.162763 | 0.0813816 | − | 0.996683i | \(-0.474067\pi\) | ||||
0.0813816 | + | 0.996683i | \(0.474067\pi\) | |||||||
\(410\) | −1.65601e7 | −0.0118664 | ||||||||
\(411\) | 2.44397e8 | 0.173640 | ||||||||
\(412\) | 6.77849e7 | 0.0477521 | ||||||||
\(413\) | 2.72048e8 | 0.190029 | ||||||||
\(414\) | 3.56280e8 | 0.246769 | ||||||||
\(415\) | 2.16816e8 | 0.148910 | ||||||||
\(416\) | −3.98287e8 | −0.271250 | ||||||||
\(417\) | −1.18862e9 | −0.802728 | ||||||||
\(418\) | 1.47071e8 | 0.0984943 | ||||||||
\(419\) | 9.08227e8 | 0.603178 | 0.301589 | − | 0.953438i | \(-0.402483\pi\) | ||||
0.301589 | + | 0.953438i | \(0.402483\pi\) | |||||||
\(420\) | −4.72786e7 | −0.0311381 | ||||||||
\(421\) | −1.47524e8 | −0.0963554 | −0.0481777 | − | 0.998839i | \(-0.515341\pi\) | ||||
−0.0481777 | + | 0.998839i | \(0.515341\pi\) | |||||||
\(422\) | −3.44124e8 | −0.222906 | ||||||||
\(423\) | −6.78797e8 | −0.436062 | ||||||||
\(424\) | −7.10797e8 | −0.452861 | ||||||||
\(425\) | −2.76814e8 | −0.174915 | ||||||||
\(426\) | −1.24393e9 | −0.779585 | ||||||||
\(427\) | 4.33576e8 | 0.269506 | ||||||||
\(428\) | −5.11184e8 | −0.315155 | ||||||||
\(429\) | −8.79606e8 | −0.537883 | ||||||||
\(430\) | 9.99912e6 | 0.00606488 | ||||||||
\(431\) | −7.39478e7 | −0.0444892 | −0.0222446 | − | 0.999753i | \(-0.507081\pi\) | ||||
−0.0222446 | + | 0.999753i | \(0.507081\pi\) | |||||||
\(432\) | 8.06216e7 | 0.0481125 | ||||||||
\(433\) | 1.77854e9 | 1.05282 | 0.526412 | − | 0.850230i | \(-0.323537\pi\) | ||||
0.526412 | + | 0.850230i | \(0.323537\pi\) | |||||||
\(434\) | 3.31656e7 | 0.0194748 | ||||||||
\(435\) | 1.70193e8 | 0.0991358 | ||||||||
\(436\) | −6.11230e8 | −0.353185 | ||||||||
\(437\) | 4.19020e8 | 0.240187 | ||||||||
\(438\) | 3.46324e8 | 0.196935 | ||||||||
\(439\) | 3.52368e9 | 1.98779 | 0.993894 | − | 0.110335i | \(-0.0351923\pi\) | ||||
0.993894 | + | 0.110335i | \(0.0351923\pi\) | |||||||
\(440\) | −1.71537e8 | −0.0960004 | ||||||||
\(441\) | −5.65437e8 | −0.313942 | ||||||||
\(442\) | 1.72268e9 | 0.948912 | ||||||||
\(443\) | −3.20313e9 | −1.75050 | −0.875248 | − | 0.483674i | \(-0.839302\pi\) | ||||
−0.875248 | + | 0.483674i | \(0.839302\pi\) | |||||||
\(444\) | −6.48135e8 | −0.351419 | ||||||||
\(445\) | 1.63840e8 | 0.0881375 | ||||||||
\(446\) | 1.02411e9 | 0.546607 | ||||||||
\(447\) | 6.49598e8 | 0.344008 | ||||||||
\(448\) | 5.73787e7 | 0.0301494 | ||||||||
\(449\) | −1.12003e8 | −0.0583939 | −0.0291969 | − | 0.999574i | \(-0.509295\pi\) | ||||
−0.0291969 | + | 0.999574i | \(0.509295\pi\) | |||||||
\(450\) | 9.11250e7 | 0.0471405 | ||||||||
\(451\) | 4.43854e7 | 0.0227836 | ||||||||
\(452\) | 1.07351e9 | 0.546790 | ||||||||
\(453\) | −1.15804e9 | −0.585304 | ||||||||
\(454\) | 7.06184e8 | 0.354179 | ||||||||
\(455\) | 3.32558e8 | 0.165511 | ||||||||
\(456\) | 9.48188e7 | 0.0468293 | ||||||||
\(457\) | −1.64644e9 | −0.806937 | −0.403469 | − | 0.914993i | \(-0.632196\pi\) | ||||
−0.403469 | + | 0.914993i | \(0.632196\pi\) | |||||||
\(458\) | 1.87802e7 | 0.00913420 | ||||||||
\(459\) | −3.48705e8 | −0.168312 | ||||||||
\(460\) | −4.88724e8 | −0.234105 | ||||||||
\(461\) | 2.01399e8 | 0.0957422 | 0.0478711 | − | 0.998854i | \(-0.484756\pi\) | ||||
0.0478711 | + | 0.998854i | \(0.484756\pi\) | |||||||
\(462\) | 1.26719e8 | 0.0597854 | ||||||||
\(463\) | −7.61645e8 | −0.356631 | −0.178316 | − | 0.983973i | \(-0.557065\pi\) | ||||
−0.178316 | + | 0.983973i | \(0.557065\pi\) | |||||||
\(464\) | −2.06552e8 | −0.0959878 | ||||||||
\(465\) | −6.39235e7 | −0.0294832 | ||||||||
\(466\) | −1.64850e9 | −0.754637 | ||||||||
\(467\) | −3.99968e9 | −1.81726 | −0.908628 | − | 0.417606i | \(-0.862869\pi\) | ||||
−0.908628 | + | 0.417606i | \(0.862869\pi\) | |||||||
\(468\) | −5.67093e8 | −0.255737 | ||||||||
\(469\) | 3.52682e8 | 0.157862 | ||||||||
\(470\) | 9.31134e8 | 0.413685 | ||||||||
\(471\) | 6.86282e8 | 0.302642 | ||||||||
\(472\) | 6.36361e8 | 0.278552 | ||||||||
\(473\) | −2.68003e7 | −0.0116446 | ||||||||
\(474\) | −4.80562e8 | −0.207265 | ||||||||
\(475\) | 1.07172e8 | 0.0458831 | ||||||||
\(476\) | −2.48175e8 | −0.105471 | ||||||||
\(477\) | −1.01205e9 | −0.426962 | ||||||||
\(478\) | −1.15567e9 | −0.483990 | ||||||||
\(479\) | −6.32298e7 | −0.0262874 | −0.0131437 | − | 0.999914i | \(-0.504184\pi\) | ||||
−0.0131437 | + | 0.999914i | \(0.504184\pi\) | |||||||
\(480\) | −1.10592e8 | −0.0456435 | ||||||||
\(481\) | 4.55899e9 | 1.86793 | ||||||||
\(482\) | 1.10494e9 | 0.449443 | ||||||||
\(483\) | 3.61034e8 | 0.145792 | ||||||||
\(484\) | −7.87415e8 | −0.315678 | ||||||||
\(485\) | −1.11265e9 | −0.442856 | ||||||||
\(486\) | 1.14791e8 | 0.0453609 | ||||||||
\(487\) | −5.49748e8 | −0.215681 | −0.107841 | − | 0.994168i | \(-0.534394\pi\) | ||||
−0.107841 | + | 0.994168i | \(0.534394\pi\) | |||||||
\(488\) | 1.01420e9 | 0.395053 | ||||||||
\(489\) | 3.54624e8 | 0.137147 | ||||||||
\(490\) | 7.75633e8 | 0.297831 | ||||||||
\(491\) | −1.91574e9 | −0.730384 | −0.365192 | − | 0.930932i | \(-0.618997\pi\) | ||||
−0.365192 | + | 0.930932i | \(0.618997\pi\) | |||||||
\(492\) | 2.86159e7 | 0.0108325 | ||||||||
\(493\) | 8.93380e8 | 0.335793 | ||||||||
\(494\) | −6.66957e8 | −0.248916 | ||||||||
\(495\) | −2.44239e8 | −0.0905101 | ||||||||
\(496\) | 7.75794e7 | 0.0285470 | ||||||||
\(497\) | −1.26053e9 | −0.460582 | ||||||||
\(498\) | −3.74659e8 | −0.135936 | ||||||||
\(499\) | −3.40227e9 | −1.22579 | −0.612897 | − | 0.790163i | \(-0.709996\pi\) | ||||
−0.612897 | + | 0.790163i | \(0.709996\pi\) | |||||||
\(500\) | −1.25000e8 | −0.0447214 | ||||||||
\(501\) | 4.50465e8 | 0.160040 | ||||||||
\(502\) | −1.15962e9 | −0.409121 | ||||||||
\(503\) | 2.78875e9 | 0.977061 | 0.488530 | − | 0.872547i | \(-0.337533\pi\) | ||||
0.488530 | + | 0.872547i | \(0.337533\pi\) | |||||||
\(504\) | 8.16975e7 | 0.0284251 | ||||||||
\(505\) | 2.37439e9 | 0.820412 | ||||||||
\(506\) | 1.30991e9 | 0.449484 | ||||||||
\(507\) | 2.29473e9 | 0.781994 | ||||||||
\(508\) | −9.43395e8 | −0.319279 | ||||||||
\(509\) | 4.26477e9 | 1.43345 | 0.716726 | − | 0.697355i | \(-0.245640\pi\) | ||||
0.716726 | + | 0.697355i | \(0.245640\pi\) | |||||||
\(510\) | 4.78334e8 | 0.159674 | ||||||||
\(511\) | 3.50946e8 | 0.116350 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | 1.35006e8 | 0.0441511 | ||||||||
\(514\) | 4.73463e8 | 0.153786 | ||||||||
\(515\) | −1.32392e8 | −0.0427108 | ||||||||
\(516\) | −1.72785e7 | −0.00553645 | ||||||||
\(517\) | −2.49569e9 | −0.794279 | ||||||||
\(518\) | −6.56785e8 | −0.207620 | ||||||||
\(519\) | −8.48019e8 | −0.266269 | ||||||||
\(520\) | 7.77905e8 | 0.242614 | ||||||||
\(521\) | −6.50138e8 | −0.201406 | −0.100703 | − | 0.994917i | \(-0.532109\pi\) | ||||
−0.100703 | + | 0.994917i | \(0.532109\pi\) | |||||||
\(522\) | −2.94094e8 | −0.0904981 | ||||||||
\(523\) | 5.09320e9 | 1.55681 | 0.778404 | − | 0.627764i | \(-0.216030\pi\) | ||||
0.778404 | + | 0.627764i | \(0.216030\pi\) | |||||||
\(524\) | −6.75889e7 | −0.0205218 | ||||||||
\(525\) | 9.23411e7 | 0.0278508 | ||||||||
\(526\) | −2.01244e9 | −0.602939 | ||||||||
\(527\) | −3.35547e8 | −0.0998658 | ||||||||
\(528\) | 2.96416e8 | 0.0876360 | ||||||||
\(529\) | 3.27225e8 | 0.0961061 | ||||||||
\(530\) | 1.38828e9 | 0.405051 | ||||||||
\(531\) | 9.06069e8 | 0.262622 | ||||||||
\(532\) | 9.60842e7 | 0.0276669 | ||||||||
\(533\) | −2.01284e8 | −0.0575790 | ||||||||
\(534\) | −2.83116e8 | −0.0804582 | ||||||||
\(535\) | 9.98407e8 | 0.281883 | ||||||||
\(536\) | 8.24978e8 | 0.231401 | ||||||||
\(537\) | −9.62764e8 | −0.268293 | ||||||||
\(538\) | −1.94342e9 | −0.538057 | ||||||||
\(539\) | −2.07890e9 | −0.571838 | ||||||||
\(540\) | −1.57464e8 | −0.0430331 | ||||||||
\(541\) | 5.43521e9 | 1.47580 | 0.737898 | − | 0.674912i | \(-0.235819\pi\) | ||||
0.737898 | + | 0.674912i | \(0.235819\pi\) | |||||||
\(542\) | −2.23896e9 | −0.604017 | ||||||||
\(543\) | −2.39476e9 | −0.641892 | ||||||||
\(544\) | −5.80520e8 | −0.154604 | ||||||||
\(545\) | 1.19381e9 | 0.315898 | ||||||||
\(546\) | −5.74661e8 | −0.151091 | ||||||||
\(547\) | 2.16765e9 | 0.566283 | 0.283141 | − | 0.959078i | \(-0.408623\pi\) | ||||
0.283141 | + | 0.959078i | \(0.408623\pi\) | |||||||
\(548\) | 5.79311e8 | 0.150376 | ||||||||
\(549\) | 1.44405e9 | 0.372459 | ||||||||
\(550\) | 3.35033e8 | 0.0858654 | ||||||||
\(551\) | −3.45883e8 | −0.0880844 | ||||||||
\(552\) | 8.44515e8 | 0.213708 | ||||||||
\(553\) | −4.86975e8 | −0.122453 | ||||||||
\(554\) | −3.31125e9 | −0.827384 | ||||||||
\(555\) | 1.26589e9 | 0.314319 | ||||||||
\(556\) | −2.81748e9 | −0.695183 | ||||||||
\(557\) | 1.50603e8 | 0.0369268 | 0.0184634 | − | 0.999830i | \(-0.494123\pi\) | ||||
0.0184634 | + | 0.999830i | \(0.494123\pi\) | |||||||
\(558\) | 1.10460e8 | 0.0269144 | ||||||||
\(559\) | 1.21537e8 | 0.0294284 | ||||||||
\(560\) | −1.12068e8 | −0.0269664 | ||||||||
\(561\) | −1.28206e9 | −0.306576 | ||||||||
\(562\) | −9.25459e8 | −0.219928 | ||||||||
\(563\) | 4.26461e9 | 1.00716 | 0.503581 | − | 0.863948i | \(-0.332015\pi\) | ||||
0.503581 | + | 0.863948i | \(0.332015\pi\) | |||||||
\(564\) | −1.60900e9 | −0.377641 | ||||||||
\(565\) | −2.09670e9 | −0.489064 | ||||||||
\(566\) | 3.80988e9 | 0.883189 | ||||||||
\(567\) | 1.16323e8 | 0.0267994 | ||||||||
\(568\) | −2.94858e9 | −0.675141 | ||||||||
\(569\) | 5.54924e9 | 1.26282 | 0.631409 | − | 0.775450i | \(-0.282477\pi\) | ||||
0.631409 | + | 0.775450i | \(0.282477\pi\) | |||||||
\(570\) | −1.85193e8 | −0.0418854 | ||||||||
\(571\) | −6.70520e9 | −1.50725 | −0.753625 | − | 0.657304i | \(-0.771697\pi\) | ||||
−0.753625 | + | 0.657304i | \(0.771697\pi\) | |||||||
\(572\) | −2.08499e9 | −0.465820 | ||||||||
\(573\) | 1.16978e9 | 0.259755 | ||||||||
\(574\) | 2.89977e7 | 0.00639989 | ||||||||
\(575\) | 9.54539e8 | 0.209390 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | 2.69994e9 | 0.585112 | 0.292556 | − | 0.956248i | \(-0.405494\pi\) | ||||
0.292556 | + | 0.956248i | \(0.405494\pi\) | |||||||
\(578\) | −7.71838e8 | −0.166256 | ||||||||
\(579\) | −8.83425e8 | −0.189145 | ||||||||
\(580\) | 4.03421e8 | 0.0858541 | ||||||||
\(581\) | −3.79659e8 | −0.0803113 | ||||||||
\(582\) | 1.92266e9 | 0.404270 | ||||||||
\(583\) | −3.72094e9 | −0.777702 | ||||||||
\(584\) | 8.20917e8 | 0.170551 | ||||||||
\(585\) | 1.10760e9 | 0.228738 | ||||||||
\(586\) | 3.19840e9 | 0.656584 | ||||||||
\(587\) | 2.93647e9 | 0.599229 | 0.299615 | − | 0.954060i | \(-0.403142\pi\) | ||||
0.299615 | + | 0.954060i | \(0.403142\pi\) | |||||||
\(588\) | −1.34029e9 | −0.271881 | ||||||||
\(589\) | 1.29911e8 | 0.0261965 | ||||||||
\(590\) | −1.24289e9 | −0.249145 | ||||||||
\(591\) | 6.81676e8 | 0.135838 | ||||||||
\(592\) | −1.53632e9 | −0.304338 | ||||||||
\(593\) | −1.37844e9 | −0.271454 | −0.135727 | − | 0.990746i | \(-0.543337\pi\) | ||||
−0.135727 | + | 0.990746i | \(0.543337\pi\) | |||||||
\(594\) | 4.22045e8 | 0.0826240 | ||||||||
\(595\) | 4.84717e8 | 0.0943363 | ||||||||
\(596\) | 1.53979e9 | 0.297920 | ||||||||
\(597\) | −4.80136e9 | −0.923536 | ||||||||
\(598\) | −5.94033e9 | −1.13594 | ||||||||
\(599\) | −3.76637e8 | −0.0716027 | −0.0358013 | − | 0.999359i | \(-0.511398\pi\) | ||||
−0.0358013 | + | 0.999359i | \(0.511398\pi\) | |||||||
\(600\) | 2.16000e8 | 0.0408248 | ||||||||
\(601\) | 2.11400e9 | 0.397232 | 0.198616 | − | 0.980077i | \(-0.436355\pi\) | ||||
0.198616 | + | 0.980077i | \(0.436355\pi\) | |||||||
\(602\) | −1.75091e7 | −0.00327096 | ||||||||
\(603\) | 1.17463e9 | 0.218167 | ||||||||
\(604\) | −2.74499e9 | −0.506888 | ||||||||
\(605\) | 1.53792e9 | 0.282351 | ||||||||
\(606\) | −4.10295e9 | −0.748931 | ||||||||
\(607\) | −8.91110e9 | −1.61723 | −0.808613 | − | 0.588340i | \(-0.799782\pi\) | ||||
−0.808613 | + | 0.588340i | \(0.799782\pi\) | |||||||
\(608\) | 2.24756e8 | 0.0405554 | ||||||||
\(609\) | −2.98019e8 | −0.0534667 | ||||||||
\(610\) | −1.98086e9 | −0.353346 | ||||||||
\(611\) | 1.13177e10 | 2.00731 | ||||||||
\(612\) | −8.26561e8 | −0.145762 | ||||||||
\(613\) | 6.31909e8 | 0.110801 | 0.0554004 | − | 0.998464i | \(-0.482356\pi\) | ||||
0.0554004 | + | 0.998464i | \(0.482356\pi\) | |||||||
\(614\) | −3.15984e9 | −0.550904 | ||||||||
\(615\) | −5.58903e7 | −0.00968889 | ||||||||
\(616\) | 3.00371e8 | 0.0517757 | ||||||||
\(617\) | −2.14564e9 | −0.367755 | −0.183877 | − | 0.982949i | \(-0.558865\pi\) | ||||
−0.183877 | + | 0.982949i | \(0.558865\pi\) | |||||||
\(618\) | 2.28774e8 | 0.0389894 | ||||||||
\(619\) | 1.84414e9 | 0.312519 | 0.156259 | − | 0.987716i | \(-0.450056\pi\) | ||||
0.156259 | + | 0.987716i | \(0.450056\pi\) | |||||||
\(620\) | −1.51522e8 | −0.0255332 | ||||||||
\(621\) | 1.20244e9 | 0.201486 | ||||||||
\(622\) | 1.63701e8 | 0.0272762 | ||||||||
\(623\) | −2.86894e8 | −0.0475350 | ||||||||
\(624\) | −1.34422e9 | −0.221475 | ||||||||
\(625\) | 2.44141e8 | 0.0400000 | ||||||||
\(626\) | −6.46480e8 | −0.105328 | ||||||||
\(627\) | 4.96366e8 | 0.0804203 | ||||||||
\(628\) | 1.62674e9 | 0.262096 | ||||||||
\(629\) | 6.64491e9 | 1.06466 | ||||||||
\(630\) | −1.59565e8 | −0.0254242 | ||||||||
\(631\) | 6.58147e9 | 1.04285 | 0.521423 | − | 0.853299i | \(-0.325402\pi\) | ||||
0.521423 | + | 0.853299i | \(0.325402\pi\) | |||||||
\(632\) | −1.13911e9 | −0.179496 | ||||||||
\(633\) | −1.16142e9 | −0.182002 | ||||||||
\(634\) | 8.26816e9 | 1.28854 | ||||||||
\(635\) | 1.84257e9 | 0.285572 | ||||||||
\(636\) | −2.39894e9 | −0.369760 | ||||||||
\(637\) | 9.42765e9 | 1.44516 | ||||||||
\(638\) | −1.08128e9 | −0.164841 | ||||||||
\(639\) | −4.19828e9 | −0.636529 | ||||||||
\(640\) | −2.62144e8 | −0.0395285 | ||||||||
\(641\) | 9.54018e9 | 1.43072 | 0.715358 | − | 0.698758i | \(-0.246264\pi\) | ||||
0.715358 | + | 0.698758i | \(0.246264\pi\) | |||||||
\(642\) | −1.72525e9 | −0.257323 | ||||||||
\(643\) | 1.86320e9 | 0.276388 | 0.138194 | − | 0.990405i | \(-0.455870\pi\) | ||||
0.138194 | + | 0.990405i | \(0.455870\pi\) | |||||||
\(644\) | 8.55785e8 | 0.126260 | ||||||||
\(645\) | 3.37470e7 | 0.00495196 | ||||||||
\(646\) | −9.72116e8 | −0.141874 | ||||||||
\(647\) | 9.48581e9 | 1.37692 | 0.688461 | − | 0.725273i | \(-0.258287\pi\) | ||||
0.688461 | + | 0.725273i | \(0.258287\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | 3.33128e9 | 0.478360 | ||||||||
\(650\) | −1.51935e9 | −0.217000 | ||||||||
\(651\) | 1.11934e8 | 0.0159011 | ||||||||
\(652\) | 8.40590e8 | 0.118773 | ||||||||
\(653\) | −6.17298e9 | −0.867559 | −0.433779 | − | 0.901019i | \(-0.642820\pi\) | ||||
−0.433779 | + | 0.901019i | \(0.642820\pi\) | |||||||
\(654\) | −2.06290e9 | −0.288374 | ||||||||
\(655\) | 1.32010e8 | 0.0183553 | ||||||||
\(656\) | 6.78302e7 | 0.00938122 | ||||||||
\(657\) | 1.16884e9 | 0.160797 | ||||||||
\(658\) | −1.63047e9 | −0.223112 | ||||||||
\(659\) | 5.38863e9 | 0.733465 | 0.366733 | − | 0.930326i | \(-0.380476\pi\) | ||||
0.366733 | + | 0.930326i | \(0.380476\pi\) | |||||||
\(660\) | −5.78937e8 | −0.0783840 | ||||||||
\(661\) | 1.44276e10 | 1.94307 | 0.971536 | − | 0.236891i | \(-0.0761284\pi\) | ||||
0.971536 | + | 0.236891i | \(0.0761284\pi\) | |||||||
\(662\) | 1.97368e9 | 0.264408 | ||||||||
\(663\) | 5.81404e9 | 0.774784 | ||||||||
\(664\) | −8.88080e8 | −0.117724 | ||||||||
\(665\) | −1.87664e8 | −0.0247461 | ||||||||
\(666\) | −2.18746e9 | −0.286932 | ||||||||
\(667\) | −3.08065e9 | −0.401978 | ||||||||
\(668\) | 1.06777e9 | 0.138599 | ||||||||
\(669\) | 3.45638e9 | 0.446303 | ||||||||
\(670\) | −1.61129e9 | −0.206972 | ||||||||
\(671\) | 5.30924e9 | 0.678427 | ||||||||
\(672\) | 1.93653e8 | 0.0246168 | ||||||||
\(673\) | 1.28631e10 | 1.62664 | 0.813321 | − | 0.581816i | \(-0.197658\pi\) | ||||
0.813321 | + | 0.581816i | \(0.197658\pi\) | |||||||
\(674\) | −6.07735e9 | −0.764548 | ||||||||
\(675\) | 3.07547e8 | 0.0384900 | ||||||||
\(676\) | 5.43935e9 | 0.677226 | ||||||||
\(677\) | 1.04145e10 | 1.28997 | 0.644986 | − | 0.764195i | \(-0.276863\pi\) | ||||
0.644986 | + | 0.764195i | \(0.276863\pi\) | |||||||
\(678\) | 3.62309e9 | 0.446452 | ||||||||
\(679\) | 1.94832e9 | 0.238845 | ||||||||
\(680\) | 1.13383e9 | 0.138282 | ||||||||
\(681\) | 2.38337e9 | 0.289186 | ||||||||
\(682\) | 4.06120e8 | 0.0490240 | ||||||||
\(683\) | 7.78284e9 | 0.934686 | 0.467343 | − | 0.884076i | \(-0.345211\pi\) | ||||
0.467343 | + | 0.884076i | \(0.345211\pi\) | |||||||
\(684\) | 3.20014e8 | 0.0382360 | ||||||||
\(685\) | −1.13147e9 | −0.134501 | ||||||||
\(686\) | −2.80025e9 | −0.331179 | ||||||||
\(687\) | 6.33831e7 | 0.00745804 | ||||||||
\(688\) | −4.09564e7 | −0.00479471 | ||||||||
\(689\) | 1.68742e10 | 1.96542 | ||||||||
\(690\) | −1.64944e9 | −0.191146 | ||||||||
\(691\) | −1.41219e10 | −1.62824 | −0.814122 | − | 0.580694i | \(-0.802781\pi\) | ||||
−0.814122 | + | 0.580694i | \(0.802781\pi\) | |||||||
\(692\) | −2.01012e9 | −0.230595 | ||||||||
\(693\) | 4.27677e8 | 0.0488146 | ||||||||
\(694\) | 1.04825e10 | 1.19044 | ||||||||
\(695\) | 5.50289e9 | 0.621790 | ||||||||
\(696\) | −6.97112e8 | −0.0783737 | ||||||||
\(697\) | −2.93380e8 | −0.0328183 | ||||||||
\(698\) | 7.68458e8 | 0.0855315 | ||||||||
\(699\) | −5.56368e9 | −0.616158 | ||||||||
\(700\) | 2.18883e8 | 0.0241195 | ||||||||
\(701\) | 4.17672e9 | 0.457955 | 0.228977 | − | 0.973432i | \(-0.426462\pi\) | ||||
0.228977 | + | 0.973432i | \(0.426462\pi\) | |||||||
\(702\) | −1.91394e9 | −0.208808 | ||||||||
\(703\) | −2.57266e9 | −0.279279 | ||||||||
\(704\) | 7.02615e8 | 0.0758950 | ||||||||
\(705\) | 3.14258e9 | 0.337772 | ||||||||
\(706\) | −4.51454e9 | −0.482834 | ||||||||
\(707\) | −4.15770e9 | −0.442471 | ||||||||
\(708\) | 2.14772e9 | 0.227437 | ||||||||
\(709\) | −3.27466e9 | −0.345068 | −0.172534 | − | 0.985004i | \(-0.555195\pi\) | ||||
−0.172534 | + | 0.985004i | \(0.555195\pi\) | |||||||
\(710\) | 5.75895e9 | 0.603864 | ||||||||
\(711\) | −1.62190e9 | −0.169231 | ||||||||
\(712\) | −6.71090e8 | −0.0696788 | ||||||||
\(713\) | 1.15707e9 | 0.119549 | ||||||||
\(714\) | −8.37591e8 | −0.0861169 | ||||||||
\(715\) | 4.07225e9 | 0.416642 | ||||||||
\(716\) | −2.28211e9 | −0.232349 | ||||||||
\(717\) | −3.90039e9 | −0.395176 | ||||||||
\(718\) | 2.03272e9 | 0.204947 | ||||||||
\(719\) | 1.34003e10 | 1.34451 | 0.672253 | − | 0.740322i | \(-0.265327\pi\) | ||||
0.672253 | + | 0.740322i | \(0.265327\pi\) | |||||||
\(720\) | −3.73248e8 | −0.0372678 | ||||||||
\(721\) | 2.31827e8 | 0.0230351 | ||||||||
\(722\) | 3.76367e8 | 0.0372161 | ||||||||
\(723\) | 3.72917e9 | 0.366968 | ||||||||
\(724\) | −5.67646e9 | −0.555895 | ||||||||
\(725\) | −7.87932e8 | −0.0767902 | ||||||||
\(726\) | −2.65753e9 | −0.257750 | ||||||||
\(727\) | −1.38074e10 | −1.33273 | −0.666363 | − | 0.745627i | \(-0.732150\pi\) | ||||
−0.666363 | + | 0.745627i | \(0.732150\pi\) | |||||||
\(728\) | −1.36216e9 | −0.130848 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −1.60335e9 | −0.152545 | ||||||||
\(731\) | 1.77145e8 | 0.0167733 | ||||||||
\(732\) | 3.42293e9 | 0.322559 | ||||||||
\(733\) | −3.61932e9 | −0.339440 | −0.169720 | − | 0.985492i | \(-0.554286\pi\) | ||||
−0.169720 | + | 0.985492i | \(0.554286\pi\) | |||||||
\(734\) | 3.65479e9 | 0.341135 | ||||||||
\(735\) | 2.61776e9 | 0.243178 | ||||||||
\(736\) | 2.00181e9 | 0.185077 | ||||||||
\(737\) | 4.31867e9 | 0.397387 | ||||||||
\(738\) | 9.65785e7 | 0.00884470 | ||||||||
\(739\) | 1.69854e9 | 0.154817 | 0.0774087 | − | 0.996999i | \(-0.475335\pi\) | ||||
0.0774087 | + | 0.996999i | \(0.475335\pi\) | |||||||
\(740\) | 3.00063e9 | 0.272208 | ||||||||
\(741\) | −2.25098e9 | −0.203239 | ||||||||
\(742\) | −2.43095e9 | −0.218455 | ||||||||
\(743\) | −4.34751e9 | −0.388848 | −0.194424 | − | 0.980918i | \(-0.562284\pi\) | ||||
−0.194424 | + | 0.980918i | \(0.562284\pi\) | |||||||
\(744\) | 2.61831e8 | 0.0233085 | ||||||||
\(745\) | −3.00740e9 | −0.266467 | ||||||||
\(746\) | −2.49759e9 | −0.220259 | ||||||||
\(747\) | −1.26447e9 | −0.110991 | ||||||||
\(748\) | −3.03896e9 | −0.265503 | ||||||||
\(749\) | −1.74827e9 | −0.152028 | ||||||||
\(750\) | −4.21875e8 | −0.0365148 | ||||||||
\(751\) | −1.90331e10 | −1.63972 | −0.819858 | − | 0.572566i | \(-0.805948\pi\) | ||||
−0.819858 | + | 0.572566i | \(0.805948\pi\) | |||||||
\(752\) | −3.81393e9 | −0.327047 | ||||||||
\(753\) | −3.91371e9 | −0.334046 | ||||||||
\(754\) | 4.90349e9 | 0.416587 | ||||||||
\(755\) | 5.36132e9 | 0.453375 | ||||||||
\(756\) | 2.75729e8 | 0.0232090 | ||||||||
\(757\) | 2.46839e8 | 0.0206813 | 0.0103407 | − | 0.999947i | \(-0.496708\pi\) | ||||
0.0103407 | + | 0.999947i | \(0.496708\pi\) | |||||||
\(758\) | −1.63321e9 | −0.136207 | ||||||||
\(759\) | 4.42094e9 | 0.367002 | ||||||||
\(760\) | −4.38976e8 | −0.0362738 | ||||||||
\(761\) | −1.69781e10 | −1.39651 | −0.698255 | − | 0.715849i | \(-0.746040\pi\) | ||||
−0.698255 | + | 0.715849i | \(0.746040\pi\) | |||||||
\(762\) | −3.18396e9 | −0.260690 | ||||||||
\(763\) | −2.09043e9 | −0.170373 | ||||||||
\(764\) | 2.77282e9 | 0.224954 | ||||||||
\(765\) | 1.61438e9 | 0.130374 | ||||||||
\(766\) | 6.33151e9 | 0.508987 | ||||||||
\(767\) | −1.51071e10 | −1.20892 | ||||||||
\(768\) | 4.52985e8 | 0.0360844 | ||||||||
\(769\) | 1.96829e10 | 1.56080 | 0.780400 | − | 0.625281i | \(-0.215015\pi\) | ||||
0.780400 | + | 0.625281i | \(0.215015\pi\) | |||||||
\(770\) | −5.86663e8 | −0.0463096 | ||||||||
\(771\) | 1.59794e9 | 0.125565 | ||||||||
\(772\) | −2.09404e9 | −0.163804 | ||||||||
\(773\) | 6.02137e9 | 0.468886 | 0.234443 | − | 0.972130i | \(-0.424673\pi\) | ||||
0.234443 | + | 0.972130i | \(0.424673\pi\) | |||||||
\(774\) | −5.83149e7 | −0.00452050 | ||||||||
\(775\) | 2.95942e8 | 0.0228376 | ||||||||
\(776\) | 4.55741e9 | 0.350108 | ||||||||
\(777\) | −2.21665e9 | −0.169521 | ||||||||
\(778\) | 2.53966e9 | 0.193351 | ||||||||
\(779\) | 1.13586e8 | 0.00860880 | ||||||||
\(780\) | 2.62543e9 | 0.198093 | ||||||||
\(781\) | −1.54355e10 | −1.15942 | ||||||||
\(782\) | −8.65827e9 | −0.647452 | ||||||||
\(783\) | −9.92568e8 | −0.0738914 | ||||||||
\(784\) | −3.17699e9 | −0.235456 | ||||||||
\(785\) | −3.17723e9 | −0.234426 | ||||||||
\(786\) | −2.28112e8 | −0.0167560 | ||||||||
\(787\) | 1.41731e10 | 1.03646 | 0.518230 | − | 0.855241i | \(-0.326591\pi\) | ||||
0.518230 | + | 0.855241i | \(0.326591\pi\) | |||||||
\(788\) | 1.61583e9 | 0.117639 | ||||||||
\(789\) | −6.79200e9 | −0.492298 | ||||||||
\(790\) | 2.22482e9 | 0.160546 | ||||||||
\(791\) | 3.67144e9 | 0.263766 | ||||||||
\(792\) | 1.00040e9 | 0.0715545 | ||||||||
\(793\) | −2.40769e10 | −1.71453 | ||||||||
\(794\) | 8.91497e9 | 0.632045 | ||||||||
\(795\) | 4.68543e9 | 0.330723 | ||||||||
\(796\) | −1.13810e10 | −0.799806 | ||||||||
\(797\) | 2.66961e10 | 1.86786 | 0.933928 | − | 0.357462i | \(-0.116358\pi\) | ||||
0.933928 | + | 0.357462i | \(0.116358\pi\) | |||||||
\(798\) | 3.24284e8 | 0.0225900 | ||||||||
\(799\) | 1.64960e10 | 1.14410 | ||||||||
\(800\) | 5.12000e8 | 0.0353553 | ||||||||
\(801\) | −9.55517e8 | −0.0656938 | ||||||||
\(802\) | 8.32063e9 | 0.569569 | ||||||||
\(803\) | 4.29741e9 | 0.292888 | ||||||||
\(804\) | 2.78430e9 | 0.188938 | ||||||||
\(805\) | −1.67146e9 | −0.112930 | ||||||||
\(806\) | −1.84172e9 | −0.123894 | ||||||||
\(807\) | −6.55903e9 | −0.439322 | ||||||||
\(808\) | −9.72550e9 | −0.648593 | ||||||||
\(809\) | 2.58931e10 | 1.71935 | 0.859676 | − | 0.510839i | \(-0.170665\pi\) | ||||
0.859676 | + | 0.510839i | \(0.170665\pi\) | |||||||
\(810\) | −5.31441e8 | −0.0351364 | ||||||||
\(811\) | −5.90009e9 | −0.388405 | −0.194203 | − | 0.980961i | \(-0.562212\pi\) | ||||
−0.194203 | + | 0.980961i | \(0.562212\pi\) | |||||||
\(812\) | −7.06415e8 | −0.0463035 | ||||||||
\(813\) | −7.55649e9 | −0.493178 | ||||||||
\(814\) | −8.04247e9 | −0.522641 | ||||||||
\(815\) | −1.64178e9 | −0.106234 | ||||||||
\(816\) | −1.95926e9 | −0.126234 | ||||||||
\(817\) | −6.85840e7 | −0.00439993 | ||||||||
\(818\) | 1.80168e9 | 0.115091 | ||||||||
\(819\) | −1.93948e9 | −0.123365 | ||||||||
\(820\) | −1.32481e8 | −0.00839082 | ||||||||
\(821\) | −6.68653e9 | −0.421696 | −0.210848 | − | 0.977519i | \(-0.567623\pi\) | ||||
−0.210848 | + | 0.977519i | \(0.567623\pi\) | |||||||
\(822\) | 1.95517e9 | 0.122782 | ||||||||
\(823\) | 1.16174e10 | 0.726454 | 0.363227 | − | 0.931701i | \(-0.381675\pi\) | ||||
0.363227 | + | 0.931701i | \(0.381675\pi\) | |||||||
\(824\) | 5.42279e8 | 0.0337658 | ||||||||
\(825\) | 1.13074e9 | 0.0701088 | ||||||||
\(826\) | 2.17638e9 | 0.134371 | ||||||||
\(827\) | 1.38198e10 | 0.849632 | 0.424816 | − | 0.905280i | \(-0.360339\pi\) | ||||
0.424816 | + | 0.905280i | \(0.360339\pi\) | |||||||
\(828\) | 2.85024e9 | 0.174492 | ||||||||
\(829\) | −1.82270e10 | −1.11115 | −0.555576 | − | 0.831465i | \(-0.687502\pi\) | ||||
−0.555576 | + | 0.831465i | \(0.687502\pi\) | |||||||
\(830\) | 1.73453e9 | 0.105295 | ||||||||
\(831\) | −1.11755e10 | −0.675557 | ||||||||
\(832\) | −3.18630e9 | −0.191803 | ||||||||
\(833\) | 1.37412e10 | 0.823695 | ||||||||
\(834\) | −9.50899e9 | −0.567614 | ||||||||
\(835\) | −2.08549e9 | −0.123967 | ||||||||
\(836\) | 1.17657e9 | 0.0696460 | ||||||||
\(837\) | 3.72802e8 | 0.0219755 | ||||||||
\(838\) | 7.26582e9 | 0.426511 | ||||||||
\(839\) | 1.50479e10 | 0.879646 | 0.439823 | − | 0.898084i | \(-0.355041\pi\) | ||||
0.439823 | + | 0.898084i | \(0.355041\pi\) | |||||||
\(840\) | −3.78229e8 | −0.0220180 | ||||||||
\(841\) | −1.47069e10 | −0.852582 | ||||||||
\(842\) | −1.18019e9 | −0.0681336 | ||||||||
\(843\) | −3.12342e9 | −0.179570 | ||||||||
\(844\) | −2.75299e9 | −0.157618 | ||||||||
\(845\) | −1.06237e10 | −0.605730 | ||||||||
\(846\) | −5.43038e9 | −0.308343 | ||||||||
\(847\) | −2.69299e9 | −0.152280 | ||||||||
\(848\) | −5.68637e9 | −0.320221 | ||||||||
\(849\) | 1.28583e10 | 0.721121 | ||||||||
\(850\) | −2.21451e9 | −0.123683 | ||||||||
\(851\) | −2.29137e10 | −1.27451 | ||||||||
\(852\) | −9.95147e9 | −0.551250 | ||||||||
\(853\) | −3.30273e9 | −0.182201 | −0.0911006 | − | 0.995842i | \(-0.529038\pi\) | ||||
−0.0911006 | + | 0.995842i | \(0.529038\pi\) | |||||||
\(854\) | 3.46861e9 | 0.190569 | ||||||||
\(855\) | −6.25026e8 | −0.0341993 | ||||||||
\(856\) | −4.08947e9 | −0.222848 | ||||||||
\(857\) | 1.50756e10 | 0.818167 | 0.409083 | − | 0.912497i | \(-0.365849\pi\) | ||||
0.409083 | + | 0.912497i | \(0.365849\pi\) | |||||||
\(858\) | −7.03684e9 | −0.380340 | ||||||||
\(859\) | 3.66462e10 | 1.97266 | 0.986331 | − | 0.164774i | \(-0.0526896\pi\) | ||||
0.986331 | + | 0.164774i | \(0.0526896\pi\) | |||||||
\(860\) | 7.99930e7 | 0.00428852 | ||||||||
\(861\) | 9.78674e7 | 0.00522549 | ||||||||
\(862\) | −5.91583e8 | −0.0314586 | ||||||||
\(863\) | 1.85096e10 | 0.980303 | 0.490151 | − | 0.871637i | \(-0.336942\pi\) | ||||
0.490151 | + | 0.871637i | \(0.336942\pi\) | |||||||
\(864\) | 6.44973e8 | 0.0340207 | ||||||||
\(865\) | 3.92602e9 | 0.206251 | ||||||||
\(866\) | 1.42283e10 | 0.744458 | ||||||||
\(867\) | −2.60495e9 | −0.135748 | ||||||||
\(868\) | 2.65325e8 | 0.0137708 | ||||||||
\(869\) | −5.96311e9 | −0.308250 | ||||||||
\(870\) | 1.36155e9 | 0.0700996 | ||||||||
\(871\) | −1.95848e10 | −1.00428 | ||||||||
\(872\) | −4.88984e9 | −0.249739 | ||||||||
\(873\) | 6.48897e9 | 0.330085 | ||||||||
\(874\) | 3.35216e9 | 0.169838 | ||||||||
\(875\) | −4.27505e8 | −0.0215731 | ||||||||
\(876\) | 2.77059e9 | 0.139254 | ||||||||
\(877\) | −1.04554e10 | −0.523412 | −0.261706 | − | 0.965148i | \(-0.584285\pi\) | ||||
−0.261706 | + | 0.965148i | \(0.584285\pi\) | |||||||
\(878\) | 2.81894e10 | 1.40558 | ||||||||
\(879\) | 1.07946e10 | 0.536099 | ||||||||
\(880\) | −1.37229e9 | −0.0678825 | ||||||||
\(881\) | 1.60550e10 | 0.791032 | 0.395516 | − | 0.918459i | \(-0.370566\pi\) | ||||
0.395516 | + | 0.918459i | \(0.370566\pi\) | |||||||
\(882\) | −4.52349e9 | −0.221990 | ||||||||
\(883\) | 2.54528e9 | 0.124415 | 0.0622076 | − | 0.998063i | \(-0.480186\pi\) | ||||
0.0622076 | + | 0.998063i | \(0.480186\pi\) | |||||||
\(884\) | 1.37814e10 | 0.670982 | ||||||||
\(885\) | −4.19476e9 | −0.203426 | ||||||||
\(886\) | −2.56250e10 | −1.23779 | ||||||||
\(887\) | −3.47758e10 | −1.67319 | −0.836594 | − | 0.547823i | \(-0.815457\pi\) | ||||
−0.836594 | + | 0.547823i | \(0.815457\pi\) | |||||||
\(888\) | −5.18508e9 | −0.248491 | ||||||||
\(889\) | −3.22645e9 | −0.154017 | ||||||||
\(890\) | 1.31072e9 | 0.0623226 | ||||||||
\(891\) | 1.42440e9 | 0.0674622 | ||||||||
\(892\) | 8.19289e9 | 0.386510 | ||||||||
\(893\) | −6.38665e9 | −0.300119 | ||||||||
\(894\) | 5.19679e9 | 0.243250 | ||||||||
\(895\) | 4.45724e9 | 0.207819 | ||||||||
\(896\) | 4.59030e8 | 0.0213188 | ||||||||
\(897\) | −2.00486e10 | −0.927493 | ||||||||
\(898\) | −8.96023e8 | −0.0412907 | ||||||||
\(899\) | −9.55115e8 | −0.0438426 | ||||||||
\(900\) | 7.29000e8 | 0.0333333 | ||||||||
\(901\) | 2.45948e10 | 1.12023 | ||||||||
\(902\) | 3.55083e8 | 0.0161104 | ||||||||
\(903\) | −5.90931e7 | −0.00267073 | ||||||||
\(904\) | 8.58806e9 | 0.386639 | ||||||||
\(905\) | 1.10868e10 | 0.497207 | ||||||||
\(906\) | −9.26435e9 | −0.413872 | ||||||||
\(907\) | −2.23850e9 | −0.0996165 | −0.0498083 | − | 0.998759i | \(-0.515861\pi\) | ||||
−0.0498083 | + | 0.998759i | \(0.515861\pi\) | |||||||
\(908\) | 5.64947e9 | 0.250442 | ||||||||
\(909\) | −1.38474e10 | −0.611499 | ||||||||
\(910\) | 2.66047e9 | 0.117034 | ||||||||
\(911\) | −2.43248e10 | −1.06595 | −0.532973 | − | 0.846132i | \(-0.678925\pi\) | ||||
−0.532973 | + | 0.846132i | \(0.678925\pi\) | |||||||
\(912\) | 7.58551e8 | 0.0331133 | ||||||||
\(913\) | −4.64900e9 | −0.202168 | ||||||||
\(914\) | −1.31715e10 | −0.570591 | ||||||||
\(915\) | −6.68541e9 | −0.288506 | ||||||||
\(916\) | 1.50241e8 | 0.00645885 | ||||||||
\(917\) | −2.31157e8 | −0.00989951 | ||||||||
\(918\) | −2.78964e9 | −0.119014 | ||||||||
\(919\) | −2.38178e10 | −1.01227 | −0.506136 | − | 0.862454i | \(-0.668926\pi\) | ||||
−0.506136 | + | 0.862454i | \(0.668926\pi\) | |||||||
\(920\) | −3.90979e9 | −0.165537 | ||||||||
\(921\) | −1.06645e10 | −0.449811 | ||||||||
\(922\) | 1.61119e9 | 0.0677000 | ||||||||
\(923\) | 6.99987e10 | 2.93011 | ||||||||
\(924\) | 1.01375e9 | 0.0422747 | ||||||||
\(925\) | −5.86060e9 | −0.243470 | ||||||||
\(926\) | −6.09316e9 | −0.252176 | ||||||||
\(927\) | 7.72112e8 | 0.0318347 | ||||||||
\(928\) | −1.65241e9 | −0.0678736 | ||||||||
\(929\) | −3.58483e9 | −0.146695 | −0.0733473 | − | 0.997306i | \(-0.523368\pi\) | ||||
−0.0733473 | + | 0.997306i | \(0.523368\pi\) | |||||||
\(930\) | −5.11388e8 | −0.0208478 | ||||||||
\(931\) | −5.32007e9 | −0.216069 | ||||||||
\(932\) | −1.31880e10 | −0.533609 | ||||||||
\(933\) | 5.52489e8 | 0.0222709 | ||||||||
\(934\) | −3.19974e10 | −1.28499 | ||||||||
\(935\) | 5.93547e9 | 0.237473 | ||||||||
\(936\) | −4.53674e9 | −0.180833 | ||||||||
\(937\) | −1.94222e10 | −0.771277 | −0.385639 | − | 0.922650i | \(-0.626019\pi\) | ||||
−0.385639 | + | 0.922650i | \(0.626019\pi\) | |||||||
\(938\) | 2.82146e9 | 0.111626 | ||||||||
\(939\) | −2.18187e9 | −0.0860002 | ||||||||
\(940\) | 7.44907e9 | 0.292519 | ||||||||
\(941\) | 8.46440e9 | 0.331156 | 0.165578 | − | 0.986197i | \(-0.447051\pi\) | ||||
0.165578 | + | 0.986197i | \(0.447051\pi\) | |||||||
\(942\) | 5.49025e9 | 0.214000 | ||||||||
\(943\) | 1.01166e9 | 0.0392867 | ||||||||
\(944\) | 5.09089e9 | 0.196966 | ||||||||
\(945\) | −5.38533e8 | −0.0207587 | ||||||||
\(946\) | −2.14402e8 | −0.00823399 | ||||||||
\(947\) | 1.07637e10 | 0.411848 | 0.205924 | − | 0.978568i | \(-0.433980\pi\) | ||||
0.205924 | + | 0.978568i | \(0.433980\pi\) | |||||||
\(948\) | −3.84449e9 | −0.146558 | ||||||||
\(949\) | −1.94884e10 | −0.740191 | ||||||||
\(950\) | 8.57375e8 | 0.0324443 | ||||||||
\(951\) | 2.79050e10 | 1.05208 | ||||||||
\(952\) | −1.98540e9 | −0.0745794 | ||||||||
\(953\) | 3.47302e10 | 1.29982 | 0.649908 | − | 0.760013i | \(-0.274807\pi\) | ||||
0.649908 | + | 0.760013i | \(0.274807\pi\) | |||||||
\(954\) | −8.09642e9 | −0.301907 | ||||||||
\(955\) | −5.41566e9 | −0.201205 | ||||||||
\(956\) | −9.24537e9 | −0.342233 | ||||||||
\(957\) | −3.64931e9 | −0.134592 | ||||||||
\(958\) | −5.05839e8 | −0.0185880 | ||||||||
\(959\) | 1.98127e9 | 0.0725400 | ||||||||
\(960\) | −8.84736e8 | −0.0322749 | ||||||||
\(961\) | −2.71539e10 | −0.986961 | ||||||||
\(962\) | 3.64719e10 | 1.32083 | ||||||||
\(963\) | −5.82271e9 | −0.210103 | ||||||||
\(964\) | 8.83952e9 | 0.317804 | ||||||||
\(965\) | 4.08993e9 | 0.146511 | ||||||||
\(966\) | 2.88828e9 | 0.103091 | ||||||||
\(967\) | −2.78429e9 | −0.0990198 | −0.0495099 | − | 0.998774i | \(-0.515766\pi\) | ||||
−0.0495099 | + | 0.998774i | \(0.515766\pi\) | |||||||
\(968\) | −6.29932e9 | −0.223218 | ||||||||
\(969\) | −3.28089e9 | −0.115840 | ||||||||
\(970\) | −8.90120e9 | −0.313146 | ||||||||
\(971\) | 1.15571e10 | 0.405117 | 0.202558 | − | 0.979270i | \(-0.435074\pi\) | ||||
0.202558 | + | 0.979270i | \(0.435074\pi\) | |||||||
\(972\) | 9.18330e8 | 0.0320750 | ||||||||
\(973\) | −9.63589e9 | −0.335349 | ||||||||
\(974\) | −4.39799e9 | −0.152510 | ||||||||
\(975\) | −5.12779e9 | −0.177180 | ||||||||
\(976\) | 8.11362e9 | 0.279345 | ||||||||
\(977\) | −2.70102e10 | −0.926609 | −0.463304 | − | 0.886199i | \(-0.653336\pi\) | ||||
−0.463304 | + | 0.886199i | \(0.653336\pi\) | |||||||
\(978\) | 2.83699e9 | 0.0969777 | ||||||||
\(979\) | −3.51308e9 | −0.119660 | ||||||||
\(980\) | 6.20507e9 | 0.210598 | ||||||||
\(981\) | −6.96229e9 | −0.235456 | ||||||||
\(982\) | −1.53259e10 | −0.516460 | ||||||||
\(983\) | −4.70303e10 | −1.57921 | −0.789606 | − | 0.613614i | \(-0.789715\pi\) | ||||
−0.789606 | + | 0.613614i | \(0.789715\pi\) | |||||||
\(984\) | 2.28927e8 | 0.00765974 | ||||||||
\(985\) | −3.15591e9 | −0.105220 | ||||||||
\(986\) | 7.14704e9 | 0.237442 | ||||||||
\(987\) | −5.50284e9 | −0.182170 | ||||||||
\(988\) | −5.33565e9 | −0.176010 | ||||||||
\(989\) | −6.10852e8 | −0.0200793 | ||||||||
\(990\) | −1.95391e9 | −0.0640003 | ||||||||
\(991\) | −1.93734e10 | −0.632336 | −0.316168 | − | 0.948703i | \(-0.602396\pi\) | ||||
−0.316168 | + | 0.948703i | \(0.602396\pi\) | |||||||
\(992\) | 6.20636e8 | 0.0201858 | ||||||||
\(993\) | 6.66118e9 | 0.215888 | ||||||||
\(994\) | −1.00843e10 | −0.325681 | ||||||||
\(995\) | 2.22285e10 | 0.715368 | ||||||||
\(996\) | −2.99727e9 | −0.0961210 | ||||||||
\(997\) | −4.62926e10 | −1.47938 | −0.739689 | − | 0.672949i | \(-0.765027\pi\) | ||||
−0.739689 | + | 0.672949i | \(0.765027\pi\) | |||||||
\(998\) | −2.72182e10 | −0.866767 | ||||||||
\(999\) | −7.38266e9 | −0.234279 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 570.8.a.b.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.8.a.b.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial |